Related papers: Small Chvatal rank
There are two main thrusts in the theory of regular and chiral polytopes: the abstract, purely combinatorial aspect, and the geometric one of realizations. This brief survey concentrates on the latter. The dimension of a faithful…
Suppose a group $G$ acts properly on a simplicial complex $\Gamma$. Let $l$ be the number of $G$-invariant vertices and $p_1, p_2, ... p_m$ be the sizes of the $G$-orbits having size greater than 1. Then $\Gamma$ must be a subcomplex of…
This paper proposes SAT-based techniques to calculate a specific normal form of a given finite mathematical structure (model). The normal form is obtained by permuting the domain elements so that the representation of the structure is…
The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations.…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
Not only is the geometry of rock fragments often well approximated by ideal convex polyhedra having few faces and vertices, but these numbers carry vital geophysical information on the fragmentation process. Despite their significance, the…
The aim of this article is to introduce standard bases of ideals in polynomial rings with respect to a class of orderings which are not necessarily semigroup orderings. Our approach generalises the concept of standard bases with respect to…
It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…
It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.
This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the…
Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…
We propose a first-order method to solve the cubic regularization subproblem (CRS) based on a novel reformulation. The reformulation is a constrained convex optimization problem whose feasible region admits an easily computable projection.…
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere positive curvature, and what structural constraints does…
In this paper we consider the cubic regularization (CR) method for minimizing a twice continuously differentiable function. While the CR method is widely recognized as a globally convergent variant of Newton's method with superior iteration…
A catalogue of simplicial hyperplane arrangements was first given by Gr\"unbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and the weak order through the poset of regions. For simplicial arrangements,…
We consider facet-Hamiltonian cycles of polytopes, defined as cycles in their skeleton such that every facet is visited exactly once. These cycles can be understood as optimal watchman routes that guard the facets of a polytope. We consider…
The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher-Krein assures the existence of SSR…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same rank, we characterize those whose order polytopes have…
General Successive Convex Relaxation Methods (SRCMs) can be used to compute the convex hull of any compact set, in an Euclidean space, described by a system of quadratic inequalities and a compact convex set which is not very complicated.…